Ring gear pumps compress a working fluid in delivering it from a low-pressure side to a high-pressure side whilst ring gear motors are powered by compressed working fluid supplied at a high-pressure side and discharged at a low-pressure side of the ring gear motor. Both kinds of ring gear machine include a running set comprising an internal spur gear with an external toothing and an external spur gear with an internal toothing. The internal toothing generally features one tooth more than the external toothing. The two toothings are meshed. When one gear is rotated relative to the other, circulating, expanding and contracting fluid cells materialize between the teeth of the internal gear and the teeth of the external gear, which in a pumping mode direct the fluid from a low-pressure side to a high-pressure side, and in a motor mode from a high-pressure side to a low-pressure side of the ring gear machine.
For such running sets, it is worth configuring the tips of the internal gear and the roots of the external gear as epicycloids, and the roots of the internal gear and the tips of the external gear as hypocycloids. The epicycloids are formed by the rolling action of a small pitch circle, which may be, but need not necessarily be, the same for the internal gear and the external gear, on the rolling circle of the internal gear and external gear, respectively. The hypocycloids are formed correspondingly, the small pitch circles on the internal gear and external gear again being advantageously the same but not necessarily so.
The clearance of the two gears should vary in accordance with speed and the pressure level of the working fluid. For a high relative speed of the gears a large clearance is desirable due to the friction and the differences in temperature between the two gears. At a low relative speed and mostly high working pressure on the high-pressure side, small clearances are desirable to minimize volumetric losses (leakage losses). However, other influencing factors exist which should be taken into account when dimensioning the clearances. Such other influencing factors are, in particular, the inevitable out-of-round of the toothing due to production never being perfect, the accuracy in rotationally mounting one or both gears and the deviation between the actual eccentricity of the gears and an eccentricity forming the basis of the calculated toothing; eccentricity in this context is understood, as usual, to be the spacing of the rolling circle axes of the gears.
DE 42 00 883 solves the problem of radial clearance by flattening the epicycloids or hypocycloids or both in combination to a certain extent in the direction of their rolling circles. To obtain the flattening, a smaller pitch circle is rolled on a large fixed circle for each cycloid, the profile of the toothing, however, being described not by a point on the circumference of the small pitch circle but by a point which is shifted from the circumference of the small pitch circle toward its center. The resulting cycloids of the toothing are interconnected by straight pieces. The tangential clearance needed at the point of full mesh, i.e. the backlash, is obtained by equidistantly offsetting the contour of at least one of the toothings obtained by the rolling action of the pitch circles. In this known type of toothing, calculating the point of transition from the epicycloids to the hypocycloids is highly involved. Apart from this, mechanical noise materializes due to discontinuous locations.
EP 1 016 784 A recommends generating the cycloids of the internal rotor and external rotor by the rolling action of four small pitch circles, each different in radius. Although this permits adjustment of a radial clearance while avoiding discontinuous locations, this is at the cost of a tangential clearance larger than the radial clearance, due to the specification in generating the epicycloids and hypocycloids. At the point of full mesh, the gap formed between the toothings from the vertex of the mating tip to the flanks of the corresponding tooth is thus widened, resulting in the toothing being problematic. An excessive backlash circumferentially results in chatter circumferentially in the region of the rolling circle because of hydraulic and dynamic forces prompting a change in flank contact. If the tangential clearance is excessive, the fluid film between the slide-rolling flanks of the gear is too thick and the shock caused by the change in flank contact is thus inadequately dampened. Chatter is inevitable especially at high speeds, low viscosity of the working fluid and large diameters of the running set. Furthermore, increasing the clearance in the direction of the flanks is detrimental to the volumetric efficiency of the ring gear machine.